Hacker News Reader

Comment by sharkbot | Hacker News Reader

This comes to mind: https://en.wikipedia.org/wiki/Aumann's_agreement_theorem

Essentially, two genuine Bayesian rationalists (with some hand wavy preconditions) cannot agree to disagree; ie, they will eventually converge onto the same understanding of an event.

View on HN

This isn't true though, the problem is there are generally more then 2 possible explanations. For instance let's imagine both of us are using an experimental telescope to observe if some event occurs. We are then looking at four possible scenarios. The telescope could work/not work correctly and the event could happen/not happen. You are confident that the telescope works correctly and also confident that the event will not occur so you give high prior probability to the first and a low to the second. I on the other hand think the telescope is rubbish and the event will almost certainly occur and do the opposite. We sit down and wait and do not observe the event. You then come to the conclusion that the event did not occur and the telescope works correctly, while I come to the reverse conclusion.

One of the "handy wavy preconditions" is that they share priors. This nearly never happens in the real world. Almost all disagreements can be traced to differing priors.

No - the precondition is that agents share common knowledge of each others' priors (not that they have the same priors).

Here's the paper I read: http://www.ma.huji.ac.il/~raumann/pdf/Agreeing%20to%20Disagr...

Here's how it starts: "Theorem: if two people have the same priors..."

Whoops, seems you are correct. I'd misunderstood this, my apologies.

Reply on news.ycombinator.com